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Graph Condensation for Large Factor Models 大系数模型的图形凝缩
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-31 DOI: 10.1134/S1064562424702090
B. N. Chetverushkin, V. A. Sudakov, Yu. P. Titov
{"title":"Graph Condensation for Large Factor Models","authors":"B. N. Chetverushkin,&nbsp;V. A. Sudakov,&nbsp;Yu. P. Titov","doi":"10.1134/S1064562424702090","DOIUrl":"10.1134/S1064562424702090","url":null,"abstract":"<p>An original method for processing large factor models based on graph condensation using machine learning models and artificial neural networks is developed. The proposed mathematical apparatus can be used to plan and manage complex organizational and technical systems, to optimize large socioeconomic objects of national scale, and to solve problems of preserving the health of the nation (searching for compatibility of medications and optimizing health care resources).</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Representations of Solutions for Volterra Integro-Differential Equations in Hilbert Spaces 希尔伯特空间中 Volterra 积分微分方程解的表示法
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-31 DOI: 10.1134/S1064562424601240
N. A. Rautian
{"title":"Representations of Solutions for Volterra Integro-Differential Equations in Hilbert Spaces","authors":"N. A. Rautian","doi":"10.1134/S1064562424601240","DOIUrl":"10.1134/S1064562424601240","url":null,"abstract":"<p>Volterra integro-differential equations with operator coefficients in Hilbert spaces are studied. Previously obtained results are used to establish the relationship between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of operator semigroups. Representations of solutions for the considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator functions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical Modeling of Nonstationary Problems Related to Laser Thermochemistry of Methane in the Presence of Catalytic Nanoparticles 催化纳米粒子存在时甲烷激光热化学相关非稳态问题的数学建模
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-31 DOI: 10.1134/S1064562424702107
E. E. Peskova
{"title":"Mathematical Modeling of Nonstationary Problems Related to Laser Thermochemistry of Methane in the Presence of Catalytic Nanoparticles","authors":"E. E. Peskova","doi":"10.1134/S1064562424702107","DOIUrl":"10.1134/S1064562424702107","url":null,"abstract":"<p>A finite-volume algorithm with splitting over physical processes is developed to model nonstationary problems of laser thermochemistry with catalytic nanoparticles in subsonic gas flows. Two-phase flows in a heated pipe with laser radiation and radical kinetics of nonoxidative methane conversion are simulated. It is shown that the conversion of methane at the outlet of the pipe is more than 60% with predominant formation of ethylene and hydrogen.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zeros of Conic Functions, Fixed Points, and Coincidences 圆锥函数的零点、定点和巧合
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-31 DOI: 10.1134/S1064562424601306
T. N. Fomenko
{"title":"Zeros of Conic Functions, Fixed Points, and Coincidences","authors":"T. N. Fomenko","doi":"10.1134/S1064562424601306","DOIUrl":"10.1134/S1064562424601306","url":null,"abstract":"<p>The concept of a conic function with operator coefficients on a conic metric space is introduced. A zero existence theorem is proved for such functions. On this basis, a fixed point theorem for a multivalued self-mapping of a conic metric space is obtained, which generalizes the recent fixed point theorem of E.S. Zhukovskiy and E.A. Panasenko for a contracting multivalued mapping of a conic metric space with an operator contracting coefficient. Coincidence theorems for two multivalued mappings of conic metric spaces are obtained, which generalize the author’s previous results on coincidences of two multivalued mappings of metric spaces.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
AI Methods in Control of Personalized General Education 控制个性化通识教育的人工智能方法
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-31 DOI: 10.1134/S1064562424702119
A. L. Semenov, A. E. Abylkassymova, T. A. Rudchenko
{"title":"AI Methods in Control of Personalized General Education","authors":"A. L. Semenov,&nbsp;A. E. Abylkassymova,&nbsp;T. A. Rudchenko","doi":"10.1134/S1064562424702119","DOIUrl":"10.1134/S1064562424702119","url":null,"abstract":"<p>The paper proposes a new approach to control the process of general education. Digital tools are used to form spaces of goals, tasks and learning activities, and to record the educational process of each student. Artificial intelligence tools are used when choosing a student’s personal goals and ways to achieve them, to make forecasts and recommendations to participants in the educational process. Big data from the entire education system and big linguistic models are used. The effects of the approach include ensuring the success of each student, objective assessment of the work of teachers and schools, and the adequacy of the succession process to higher education.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1064562424702119.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotics for Eigenvalues of Schrödinger Operator with Small Translation and Dirichlet Condition 具有小平移和狄利克特条件的薛定谔算子特征值的渐近性
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-17 DOI: 10.1134/S1064562424702077
D. I. Borisov, D. M. Polyakov
{"title":"Asymptotics for Eigenvalues of Schrödinger Operator with Small Translation and Dirichlet Condition","authors":"D. I. Borisov,&nbsp;D. M. Polyakov","doi":"10.1134/S1064562424702077","DOIUrl":"10.1134/S1064562424702077","url":null,"abstract":"<p>We consider a non-self-adjoint Schrödinger operator on the unit interval with Dirichlet conditions perturbed by an operator of small translation. The main result is a three-term asymptotic expansion for the eigenvalues with respect to their index, and this asymptotics is uniform in the small translation. We also show that the system of eigenfunctions and generalized eigenfunctions of the considered operators forms a Bari basis in the space of square integrable functions on the considered unit interval.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical Model of Thermocurrents Based on Calculation of Electrical Resistance and Thermopower As an Integral over Electron Energy 基于电子能量积分的电阻和热功率计算的热流数学模型
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-17 DOI: 10.1134/S1064562424601070
G. G. Lazareva, V. A. Popov, V. A. Okishev, A. V. Burdakov
{"title":"Mathematical Model of Thermocurrents Based on Calculation of Electrical Resistance and Thermopower As an Integral over Electron Energy","authors":"G. G. Lazareva,&nbsp;V. A. Popov,&nbsp;V. A. Okishev,&nbsp;A. V. Burdakov","doi":"10.1134/S1064562424601070","DOIUrl":"10.1134/S1064562424601070","url":null,"abstract":"<p>We consider a model of current distribution in a tungsten sample and a vapor layer produced when the surface is heated by an electron beam. The model is based on solving electrodynamic equations and a two-phase Stefan problem in cylindrical coordinates. Based on the temperature distribution in the computational domain, the electrical resistance and thermopower are calculated via an integral over the electron energy at each grid node. The electromagnetic field configuration is a possible source of rotation of the substance, which is observed in experiments. The simulation results demonstrate the role of thermionic emission and the way of model development. The model parameters are taken from experiments at the Beam of Electrons for materials Test Applications (BETA) facility created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Upwind Bicompact Schemes for Hyperbolic Conservation Laws 双曲守恒定律的上风双紧凑方案
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-17 DOI: 10.1134/S1064562424702089
M. D. Bragin
{"title":"Upwind Bicompact Schemes for Hyperbolic Conservation Laws","authors":"M. D. Bragin","doi":"10.1134/S1064562424702089","DOIUrl":"10.1134/S1064562424702089","url":null,"abstract":"<p>Upwind bicompact schemes of third-order approximation in space are presented for the first time. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with Runge–Kutta time stepping. Stability and monotonicity of a scheme of first order in time are investigated, and the dissipative and dispersion properties of a scheme of third order in time are analyzed. Advantages of the new schemes over their centered counterparts are demonstrated.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multidimensional Fourier Interpolation and Fast Fourier Transforms 多维傅里叶插值和快速傅里叶变换
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-07-17 DOI: 10.1134/S1064562424702065
Yu. A. Basalov, N. N. Dobrovolsky, V. N. Chubarikov
{"title":"Multidimensional Fourier Interpolation and Fast Fourier Transforms","authors":"Yu. A. Basalov,&nbsp;N. N. Dobrovolsky,&nbsp;V. N. Chubarikov","doi":"10.1134/S1064562424702065","DOIUrl":"10.1134/S1064562424702065","url":null,"abstract":"<p>It is proved that the coefficients of the interpolation polynomial over a parallelepipedal grid for a multidimensional function are equal to the coefficients of the interpolation polynomial over a uniform grid for a one-dimensional function. These coefficients can be obtained by applying the fast Fourier transform based on various schemes.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Vandermonde Matrix in the Commutative Case 交换情况下的凡德蒙德矩阵
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-20 DOI: 10.1134/S1064562424702041
A. I. Perov, I. D. Kostrub
{"title":"The Vandermonde Matrix in the Commutative Case","authors":"A. I. Perov,&nbsp;I. D. Kostrub","doi":"10.1134/S1064562424702041","DOIUrl":"10.1134/S1064562424702041","url":null,"abstract":"<p>In a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde matrix are formulated and proved. Necessary and sufficient conditions for the invertibility of the Vandermonde matrix are given. Analogues of Sylvester’s theorem are formulated.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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